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TECHNICAL PAPERS

# An Enhanced Ray-Shooting Approach to Force-Closure Problems

[+] Author and Article Information
Yu Zheng

Robotics Institute,  Shanghai Jiao Tong University, Shanghai 200030, Chinayuzheng007@sjtu.edu.cn

Wen-Han Qian

Robotics Institute,  Shanghai Jiao Tong University, Shanghai 200030, Chinawhqian@sh163.net

J. Manuf. Sci. Eng 128(4), 960-968 (Jun 24, 2006) (9 pages) doi:10.1115/1.2336259 History: Received August 31, 2005; Revised June 24, 2006

## Abstract

Force-closure is a fundamental topic in grasping research. Relevant problems include force-closure test, quality evaluation, and grasp planning. Implementing the well-known force-closure condition that the origin of the wrench space lies in the interior of the convex hull of primitive wrenches, Liu presented a ray-shooting approach to force-closure test. Because of its high efficiency in 3D work space and no limitation on the contact number of a grasp, this approach is advanced. Achieving some new results of convex analysis, this paper enhances the above approach in three aspects. (a) The exactness is completed. In order to avoid trouble or mistakes, the dimension of the convex hull of primitive wrenches is taken into account, which is always ignored until now. (b) The efficiency is increased. A shortcut which skips some steps of the original force-closure test is found. (c) The scope is extended. Our simplified ray-shooting approach yields a grasp stability index suitable for grasp planning. Numerical examples in fixturing and grasping show the enhancement superiority.

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Topics: Force , Algorithms

## Figures

Figure 1

Linearization of the friction cone at a contact point

Figure 2

The polar set of a compact convex set containing the origin as a relative interior point

Figure 3

Illustration of Theorem 5. The point pS*(z)−1z is on the relative boundary of S.

Figure 4

Classification of W. (a) dimW<6 and 0∉affW. (b) dimW<6 and 0∊affW. (c) dimW=6 and 0∉riW. (d) dimW=6 and 0∊riW.

Figure 5

Logic relations among various force-closure conditions in Sec. 4

Figure 6

Point −p(−wc)−1wc+wc is the intersection of the ray Ṙ with the relative boundary of W. (a) If p(−wc)⩾1, then 0∉riW. (b) If 0<p(−wc)<1, then 0∊riW.

Figure 7

Gold ingot used as money in feudal China

Figure 8

Towards an optimal grasp on a jar. The dots indicate the initial positions of the fingertips. During the optimization, they trace three curves on the jar surface up to the optimal grasp configuration.

Figure 9

p(−wc) versus the iteration number in Example 2

## Errata

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